Cargo Measurement and Calculation



This chapter discusses the methods of calculating shipped quantities of liquefied gas cargoes. It clarifies the two main points of difference between calculations for liquefied gas and other petroleum cargoes. In the case of gas cargoes, it is first necessary to quantify both liquids and vapours and, secondly, because gas cargoes are carried in closed containers, special procedures must be adopted to derive weight-in-air.

For further reading on this subject a study of Reference 2.20 is recommended.

8.1 PRINCIPLES FOR LIQUEFIED GASES

8.1.1 Special practices for gas cargoes

The quantity of liquefied gas cargoes loaded to, or discharged from, ships is measured and calculated in a similar manner to other bulk liquid cargoes such as crude oils and petroleum products. This is done by finding cargo volume and cargo density and, after correcting both to the same temperature, by multiplying the two to obtain the cargo quantity. However, unlike most other bulk liquids carried by sea, liquefied gases are carried as boiling liquids in equilibrium with their vapours. Furthermore, they are contained within closed systems. This method of carriage involves the following considerations which lead to more complicated measurement and calculation procedures than is the case for other bulk liquids.

The inclusion of vapour in cargo calculations

At all times when cargo is in the tank, vapour spaces contain the saturated vapour of the cargo liquid. The vapour evaporates from, or condenses back into, the liquid during cargo handling and no vapour is lost to atmosphere. The vapour is, therefore, an intrinsic part of the cargo and must be accounted for in cargo quantification.

The difference between before and after quantities

On discharge, it is common practice in some trades to retain on board a significant quantity of liquid (heel) and its associated vapour to keep cargo tanks cool on the ballast voyage and to provide suitable cargo quantities for cool-down before loading the next cargo. On loading, the new cargo is added to the heel. Alternatively, if the ship has arrived with warm tanks, bulk cargo is added to the product put on board for tank cool-down purposes. Thus, at both discharge and loading, it is necessary to measure


the vapour and liquid content both before and after handling, in order to find the cargo discharged or loaded.

Temperature and liquid level measurement

Cargo loaded in a ship's tank may vary in temperature over the loading period. This may be due to cargo coming from different shore tanks or to initial cooling of shore pipelines. Liquefied gases have comparatively large thermal coefficients of volumetric expansion. These are some three to four times those of petroleum products. Accordingly, the resultant variation in density of the cargo may give rise to stratifi­cation in a ship's tank after loading. A number of temperature sensors are usually provided at different tank levels and it is important that all these temperature readings are taken into account to assess accurate averages for the liquid and vapour. It is from these average temperatures that the appropriate temperature corrections may be applied.

Either by boil-off or by condensation, a tank's liquid and vapour content will adjust to saturated equilibrium. However, this equilibrium may not be achieved immediately after loading. It is, therefore, desirable to delay cargo measurement and sampling for as long as possible, subject to the constraints of the ship's departure time.

8.1.2 General - Density in Air and Density in Vacuo

Liquefied gas cargo quantities are commonly expressed in terms of "weight in air" — often as a result of Customs regulations. But no air is physically displaced from closed liquefied gas systems, and we include both vapour and liquid in our quantification. So, the expression "weight in air" can be confusing and we must clarify the fundamental concept.

The terms "weight" and "mass" are often used interchangeably. This is not correct. The "mass" is the amount of matter in any given object, whereas its "weight" is the force exerted by gravity on the object. The mass is a characteristic of an object — it would be the same in space (i.e. zero gravity) as on earth, while the weight is dependent on the force of gravity where the object is placed.

Mass is the only Sl unit not based upon fundamental atomic properties or the speed of light. The reference standard is a small platinum cylinder with a mass of exactly 1 kilogram made in the late 1880's; it is kept under inert conditions at the Bureau International des Poids et Mesures near Paris. Copies are kept in various laboratories around the world as a comparison standard.

Everyday commodities are sold by weight, for example fruit or cement. This means their weight-in-air. Consider a simple beam balance. Weighing is carried out by balancing the force of gravity acting on the commodity against the force of gravity acting on a known mass — for example a brass weight. Since the gravitational force is the same on both sides of the balance, then this weighing process is balancing mass against mass.

However, the commodity and the brass weight are immersed in air during this process and — by Archimedes principle — there will be a small upthrust. The upthrust is equal to the force of gravity acting on the mass of air displaced. So, if the commodity and the weight occupied the same volume, then the buoyancy upthrust would be the same — so the result would be a mass to mass balance. The same would apply if the weighing was carried out in a perfect vacuum; so, the term weight-in-vacuum is synonymous with mass.


It is most usual for the volume of the commodity being weighed on the beam balance to be different to the volume of the brass weights. So, there is an imbalance in the buoyancy forces on either side of the balance. This is usually ignored as it is so small, but the result is that the weight of a commodity determined by this method is slightly different to its actual mass. To minimise the effect of buoyancy variations, the balance weights are standardised against brass which has a density of 8,000 kg/m3. So, the use of balance weights made of a different material does not matter as all balance weights are calibrated against a brass standard which thereby compensates for the different buoyancy.

The type of weighing machine does not matter since all devices are calibrated in accordance with the standards described. Variation in the gravitational field have no effect on the result as the variation affects both sides of the balance equally. So, the result is independent of the type of machine used in its location. Of course, if a machine is calibrated under one gravitational field and is then relocated to an area with a different gravitational field, then the results will be incorrect unless it is recalibrated.

The above description of quantification applies to any weighing, whether it be apples or crude oil. However, it is clearly impractical to place a ship on a beam balance, so the cargo is quantified indirectly by taking a small sample of the cargo and determining its density — which is its mass per unit volume. If this density is multiplied by the cargo volume, then the quantity of the whole cargo can be obtained.

8.1.3 True Density - Apparent Density

There are two important points to note when applying this indirect method. Density should be quoted in the fundamental units of mass per unit volume; this is also called "true density". It is the weight per unit volume in a vacuum. So, an adjustment for the bouyancy of air is necessary to obtain the weight-in-air. Conversely, the "apparent density" of a substance is the weight per unit volume in air. Both densities are quoted in the same units (e.g. kilograms per litre) but, as the cargoes are traded by quantity-in-air or quantity-in-vacuum, it is essential to specify density units clearly.

8.1.4 Relative Density (Specific Gravity)

The density of a substance relative to that of pure water is also an important unit in our industry. This is called the "relative density" or "specific gravity". Again we must account for bouyancy and also for the fact that the water may be at a different temperature to the substance under consideration.

The "relative density" or "specific gravity" of a liquid is the ratio of the weight in vacuo of a given volume of that liquid at a specified temperature to the weight in vacuo of an equal volume of pure water at a specified temperature. When this ratio is reported, the reference temperatures must also be stated. For example, relative density 15°C/20°C means the ratio of the true density of the liquid at 15°C to the true density of water at 20°C.


8.1.5 Apparent Relative Density (Apparent Specific Gravity)

The "apparent relative density" or "apparent specific gravity" of a liquid is the ratio of the weight in air of a given volume of that liquid at a specified temperature to the weight in air of an equal volume of pure water at a specified temperature. When this ratio is reported, the reference temperatures must also be stated. For example, apparent relative density 15°C/20°C means the ratio of the apparent density of the liquid at 15°C to the apparent density of water at 20°C.

It is obvious that the volume of the cargo is very important, and this is in turn dependent on its temperature. So, it is necessary to specify the conditions of the cargo at which it is to be quantified. The condition most commonly chosen is to evaluate the cargo as though it was at 15°C; it is further assumed that the entire cargo is a liquid at its boiling point.

It is now clear why it is essential to state clearly the standard condition assumed for the cargo quantification. Although the mass of two cargoes may be identical, if their volumes are not equal, the upthrust caused by air displacement will be different and hence their weight will be different. An extreme case could be conceived in which two cargoes of equal mass were weighed, one entirely as a liquid, and the other entirely as a vapour. The former would have a weight not greatly different in magnitude from its mass; whilst the latter would have very little weight due to its very large air displacement. The use of a precise standard avoids this ambiguity.

The derivation of cargo weight may be carried out in practice by two methods. The mass may be calculated and this converted to weight by use of a conversion factor, with the liquid density at 15°C. The conversion factor used in this method is given by the short table at the introduction to Table 56 of the ASTM/IP Petroleum Measurement Tables.

The second practical method of determining the weight of a cargo is from its volume at 15°C using a volume to weight conversion factor. This weight conversion factor is the weight per unit volume of the saturated liquid at 15°C. This factor should not be confused with density, although it is closely related. The factor has a unit of weight per unit volume, whilst true density has a unit of mass per unit volume. The main Table 56 gives the relationship between density at 15°C and this volume to weight conversion factor.

Liquefied gases are always handled in closed containers from which air is totally excluded. Consequently, air has no influence on either the liquid phase or the vapour phase of the stored product.

Although from a purely scientific point of view, it is not correct to use apparent densities in quantity calculations, they are applied in the commercial trade of liquefied gases. An apparent density of a liquefied gas should be considered as a theoretical density. It may be obtained from a True Density, converted to Apparent Density by applying ASTM Table 56. Densities of the most common liquefied gases at their boiling point vary from 0.5680 Kg/Litre (Ethylene) to 0.9714 Kg/Litre (Vinyl Chloride Monomer). When converting this true density to density in air (Apparent density), always a difference of 0.0011 Kg/Litre appears. Note that conversion from density in air to density in vacuo has to be done by introducing the conversion factors from ASTM Table 56 with a density at 15°C. This conversion is not always possible considering the critical temperature of some products such as Ethylene, Methane, ... which are completely gaseous at 15°C.


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